The Ground and Low Lying Excited States of the Two-Dimensional Hubbard Model

TL;DR

This study investigates the 2D Hubbard model's ground state using quantum Monte Carlo, revealing a spin gap, incommensurate peaks, and signs of d-wave superconductivity, with implications for understanding high-temperature superconductors.

Contribution

It provides new insights into the ground state properties of the 2D Hubbard model, especially regarding spin excitations and superconducting correlations, using advanced quantum Monte Carlo methods.

Findings

Spin excitation gap in the ground state

Incommensurate peaks in spin correlation function

Enhanced d-wave superconducting correlations

Abstract

We have studied the ground state of the two-dimensional (2D) Hubbard model by using a quantum monte method paying special attention to the shell structure effect on finite size clusters. Our calculations show there is a gap for spin excitations in the ground state and incommensurate peaks at $(\pi \pm \delta, \pi)$ and $(\pi, \pi \pm \delta)$ in the spin correlation function for a low lying excited state. In the ground state, the long range part of the d-wave superconducting correlation function is enhanced and the momentum distribution function at the Fermi level $(\pi,0)$ is rounded. The gap in spin excitations and the momentum distribution function rounding is consistent with opening a d-wave superconducting gap in the ground state.